How to Find the Wind Component Parallel to a Dash Vector?

[-EquinoX-]

Homework Statement

A 100 meter dash is run on a track in the direction of the vector v = 4i + 7j. The wind velocity w is 5i + j km/hr. The rules say that a legal wind speed measured in the direction of the dash must not exceed 5 km/hr.

Find the component of w which is parallel to v.

Homework Equations

The Attempt at a Solution

I have no idea to solve this problem

 

[Hootenanny]

Homework Statement

A 100 meter dash is run on a track in the direction of the vector v = 4i + 7j. The wind velocity w is 5i + j km/hr. The rules say that a legal wind speed measured in the direction of the dash must not exceed 5 km/hr.

Find the component of w which is parallel to v.

Homework Equations

The Attempt at a Solution

I have no idea to solve this problem

You must have some idea. Which operation gives to the component of one vector that is parallel to another?

 

[-EquinoX-]

it's parallel to one another if it's angle between them is 0 right?

so therefore using the geometric of vectors:

v . w = |v| * |w|, right?

 

[gabbagabbahey]

it's parallel to one another if it's angle between them is 0 right?

so therefore using the geometric of vectors:

v . w = |v| * |w|, right?

Sure, if v . w = |v| * |w| then w and v are parallel; but that's not what Hootenanny was asking.

Suppose you want to find 'the component of w' that is parallel to v...how would you do that?

 

[Hootenanny]

it's parallel to one another if it's angle between them is 0 right?

so therefore using the geometric of vectors:

v . w = |v| * |w|, right?

That is correct. However, it is perhaps more useful to note that:

$$\mathbf{v}\cdot\left(\frac{\mathbf{w}}{\left\|\mathbf{w}\right\|}\right) = \left|\mathbf{v}\right|\cos\theta$$

That is, if u is a unit vector then the scalar product v.u gives the projection of v in the direction u.

Edit:

but that's not what Halls was asking.

 

[-EquinoX-]

hmmm...so how do I apply this to the question?

 

[gabbagabbahey]

but that's not what Hootenanny was asking.

 

[-EquinoX-]

Is this question asking for a new wind speed/vector which is parallel to v

 

[Hootenanny]

Is this question asking for a new wind speed/vector which is parallel to v

No. The question is asking for the component of w that is parallel to v. Can you use the hints I have you in post number 5 to solve this problem?

 

[-EquinoX-]

No. The question is asking for the component of w that is parallel to v. Can you use the hints I have you in post number 5 to solve this problem?

No, I don't...

 

[Hootenanny]

No, I don't...

I don't know how I can make it clearer without explicitly giving you the answer. Pay particular attention the the last paragraph in on of my previous posts.

That is correct. However, it is perhaps more useful to note that:

$$\mathbf{v}\cdot\left(\frac{\mathbf{w}}{\left\|\mathbf{w}\right\|}\right) = \left|\mathbf{v}\right|\cos\theta$$

That is, if u is a unit vector then the scalar product v.u gives the projection of v in the direction u.

 

[-EquinoX-]

what is u related to my question?

 

[-EquinoX-]

why is it v . w/||W|| not w . v/||v||

 

[gabbagabbahey]

why is it v . w/||W|| not w . v/||v||

v . w/||W|| gives the component of v parallel to w.

w . v/||v|| gives the component of w parallel to v.

Since you are trying to find the component of the wind speed w parallel to the velocity v; you will indeed want to use w . v/||v|| for your problem.

 

[-EquinoX-]

v . w/||W|| gives the component of v parallel to w.

w . v/||v|| gives the component of w parallel to v.

Since you are trying to find the component of the wind speed w parallel to the velocity v; you will indeed want to use w . v/||v|| for your problem.

ok thanks! I got it now